Subgroups — C₄×C₇×C₃₁×C₃₇ #44545786

Order 32116.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃₁×C₃₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₃₁×C₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃₁×C₃₇	C₂×C₇	1	1	yes	characteristic
5	C₃₁×C₃₇	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₇×C₃₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₇×C₃₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₃₇	C₂×C₃₁	1	1	yes	characteristic
9	C₂×C₇×C₃₁	C₂×C₃₇	1	1	yes	characteristic
10	C₇×C₃₇	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₃₁	C₄×C₃₇	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₃₇	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₃₁	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₇	C₂×C₇×C₃₁	1	1	yes	characteristic
15	C₂×C₃₁	C₂×C₇×C₃₇	1	1	yes	characteristic
16	C₃₇	C₄×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₁	C₄×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₇	C₃₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇	C₂×C₃₁×C₃₇	1	1	yes	characteristic
20	C₇	C₄×C₃₁×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₇×C₃₁×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₃₁×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₃₁×C₃₇
socle, prime radical	C₂×C₇×C₃₁×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇×C₃₁×C₃₇	C₄	direct (N × H)
3. C₄×C₃₁×C₃₇	C₇	direct (N × H)
5. C₃₁×C₃₇	C₄×C₇	direct (N × H)
6. C₄×C₇×C₃₇	C₃₁	direct (N × H)
7. C₄×C₇×C₃₁	C₃₇	direct (N × H)
10. C₇×C₃₇	C₄×C₃₁	direct (N × H)
11. C₇×C₃₁	C₄×C₃₇	direct (N × H)
12. C₄×C₃₇	C₇×C₃₁	direct (N × H)
13. C₄×C₃₁	C₇×C₃₇	direct (N × H)
16. C₃₇	C₄×C₇×C₃₁	direct (N × H)
17. C₃₁	C₄×C₇×C₃₇	direct (N × H)
18. C₄×C₇	C₃₁×C₃₇	direct (N × H)
20. C₇	C₄×C₃₁×C₃₇	direct (N × H)
21. C₄	C₇×C₃₁×C₃₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×C₃₁×C₃₇	2
C₄×C₃₁×C₃₇	7
C₄×C₇×C₃₇	31
C₄×C₇×C₃₁	37

Subgroups — C4×C7×C31×C37 #44545786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₃₁×C₃₇ #44545786